Forty Hectares of Common Land: Reading a Village Production Possibility Frontier
The gram panchayat of a block in Sitamarhi district owns 40 hectares of common land, all of it now under paddy, producing 1,040 quintals a year. A fisheries cooperative wants pond land. The block agriculture officer estimates that converting the land in 10-hectare steps would give this pattern of output - paddy (quintals): 1,040, 960, 850, 700, 500; fish (quintals): 0, 400, 820, 1,220, 1,520. The lowest-lying plots nearest the stream would be converted first. Local prices are ₹1,800 per quintal of paddy and ₹400 per quintal of fish. Last year the panchayat actually produced 950 quintals of paddy and 250 quintals of fish, because 6 hectares lay fallow after a boundary dispute and the pumps ran only half the season. Three people react to the proposal. The cooperative secretary says converting all 40 hectares is obviously best because fish output is then at its highest. The chairperson says ancestral paddy land must never be converted. Another member says the all-pond plan will yield 1,520 quintals of fish.
1. Calculate the marginal opportunity cost of each successive 10-hectare conversion, explain the shape of the production possibility frontier implied by this data, and locate last year's actual output (950 quintals of paddy, 250 quintals of fish) relative to the frontier.
Read the worked answer
Marginal opportunity cost (MOC) = paddy sacrificed ÷ fish gained.
| Conversion | Paddy lost (q) | Fish gained (q) | MOC (q paddy per q fish) |
|---|---|---|---|
| 0 → 10 ha | 80 | 400 | 0.20 |
| 10 → 20 ha | 110 | 420 | 0.26 |
| 20 → 30 ha | 150 | 400 | 0.375 |
| 30 → 40 ha | 200 | 300 | 0.67 |
MOC rises at every step, so the frontier is concave to the origin (bowed outward). The reason is that land is not homogeneous: the wet, low-lying plots give a large fish yield and would have given only a modest paddy yield, so they are converted first. As conversion moves on to better paddy land, each extra quintal of fish costs more and more paddy.
Last year's bundle (950 paddy, 250 fish) lies inside the frontier. At 960 quintals of paddy the panchayat could have had 400 quintals of fish; getting only 250 quintals of fish alongside 950 quintals of paddy means resources were idle or badly used (fallow hectares, half-season pumping). It is attainable but inefficient. A point outside the frontier is unattainable with the present land, water and technique.
2. Value the output at each of the five points using the given prices and advise the panchayat. Does the cooperative secretary's reasoning survive this test?
Read the worked answer
| Land to ponds | Paddy value (₹) | Fish value (₹) | Total (₹) |
|---|---|---|---|
| 0 ha | 18,72,000 | 0 | 18,72,000 |
| 10 ha | 17,28,000 | 1,60,000 | 18,88,000 |
| 20 ha | 15,30,000 | 3,28,000 | 18,58,000 |
| 30 ha | 12,60,000 | 4,88,000 | 17,48,000 |
| 40 ha | 9,00,000 | 6,08,000 | 15,08,000 |
The maximum value is at 10 hectares converted (₹18.88 lakh), not at 40 hectares. The secretary's argument fails because it confuses the largest quantity of one good with the largest value of output. Every one of the five points is on the frontier, so all are productively efficient; efficiency does not by itself tell you which point is worth choosing. The all-pond plan is efficient and yet the worst of the five by value, because it sacrifices 1,040 quintals of paddy worth ₹18.72 lakh to gain fish worth ₹6.08 lakh.
The ranking is price-sensitive, so the advice must be conditional. If the fish price doubled to ₹800 a quintal, 30 hectares would become the best point - the choice depends on relative prices, not on the physical maximum of either product.
3. Classify each of the three statements as positive or normative, and explain what economics can and cannot settle in this dispute.
Read the worked answer
Cooperative secretary: mixed. "The all-pond plan yields 1,520 quintals of fish, the highest of the five" is a positive statement - it can be checked against the officer's estimates. "Is obviously best" smuggles in a valuation and is normative, and it is also factually wrong once relative prices are used.
Chairperson: purely normative. "Must never be converted" is a value judgement about tradition, inheritance and food security; no data set can confirm or refute it.
The member: positive. The figure 1,520 quintals is verifiable.
Economics can test the positive parts - compute the opportunity costs, value the bundles, show that 950 paddy with 250 fish is inside the frontier, and show how the ranking changes when the fish price changes. It cannot decide how much weight to give ancestral occupation, risk of a new enterprise, or the village's preference for food grain over cash income. The defensible procedure is to state the cost of each option honestly and then let the panchayat's political choice, not the economist's, decide among efficient points.